The first thing about a BX 2360, there is no "steering box" on the machine.
There is no mechanical connection between the steering wheel and the front wheels.
The only connection from up front to the steering wheel/valve is several hydraulic pipes/hoses.
With the engine off, the steering valve acts like a "primitive" hydraulic pump and allows you some
basic high effort steering control in the event the engine quits.
I would have an assistant turn the steering wheel back and forth while I laid on the ground
in front of the tractor. You shouldn't see any "play" or lost motion in the mechanical steering linkage.
Check that the hydraulic steering cylinder is firmly attached.
Check the inner tie rod ends for play/lost motion.
Check the outer tie rod ends for play/lost motion.
Check that the taper studs/castle nuts on the outer tie rod ends are not loose in the cast iron steering knuckles.
Jack up both front wheels and give them a shake. (side to side and up/down)
If you can't find anything mechanical loose, then unfortunately, you have a bad steering cylinder or steering valve. The steering cylinder can be rebuilt if it's faulty, but if worn sufficiently inside the aluminum housing where the seals slide, the unit will require replacement.
Free Workshop manual here:
https://www.kubotabooks.com/AutoIndex/index.php?dir=Tractor Owners Manuals/
Let us know what you find.